examples: Added Andriy's first set of examples

bug: added Andriy insertrow fix

src/Examples/Examples.csproj

@@ -10,7 +10,7 @@
     <AppDesignerFolder>Properties</AppDesignerFolder>
     <RootNamespace>Examples</RootNamespace>
     <AssemblyName>Examples</AssemblyName>
-    <TargetFrameworkVersion>v3.5</TargetFrameworkVersion>
+    <TargetFrameworkVersion>v4.0</TargetFrameworkVersion>
     <FileAlignment>512</FileAlignment>
     <FileUpgradeFlags>
     </FileUpgradeFlags>
@@ -31,6 +31,7 @@
     <IsWebBootstrapper>false</IsWebBootstrapper>
     <UseApplicationTrust>false</UseApplicationTrust>
     <BootstrapperEnabled>true</BootstrapperEnabled>
+    <TargetFrameworkProfile />
   </PropertyGroup>
   <PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Debug|AnyCPU' ">
     <DebugSymbols>true</DebugSymbols>
@@ -56,6 +57,7 @@
     <Reference Include="System.Core">
       <RequiredTargetFramework>3.5</RequiredTargetFramework>
     </Reference>
+    <Reference Include="System.Numerics" />
     <Reference Include="System.Xml.Linq">
       <RequiredTargetFramework>3.5</RequiredTargetFramework>
     </Reference>
@@ -66,6 +68,24 @@
     <Reference Include="System.Xml" />
   </ItemGroup>
   <ItemGroup>
+    <Compile Include="IExample.cs" />
+    <Compile Include="LinearAlgebra\DirectSolvers.cs" />
+    <Compile Include="LinearAlgebra\Factorization\Cholesky.cs" />
+    <Compile Include="LinearAlgebra\Factorization\Evd.cs" />
+    <Compile Include="LinearAlgebra\Factorization\LU.cs" />
+    <Compile Include="LinearAlgebra\MatrixNorms.cs" />
+    <Compile Include="LinearAlgebra\Factorization\QR.cs" />
+    <Compile Include="LinearAlgebra\Factorization\Svd.cs" />
+    <Compile Include="LinearAlgebra\MatrixArithmeticOperations.cs" />
+    <Compile Include="LinearAlgebra\MatrixDataAccessor.cs" />
+    <Compile Include="LinearAlgebra\MatrixInitialization.cs" />
+    <Compile Include="LinearAlgebra\MatrixRowColumnOperations.cs" />
+    <Compile Include="LinearAlgebra\MatrixSpecialNumbers.cs" />
+    <Compile Include="LinearAlgebra\MatrixTransposeAndInverse.cs" />
+    <Compile Include="LinearAlgebra\MatrixTriangular.cs" />
+    <Compile Include="LinearAlgebra\VectorArithmeticOperations.cs" />
+    <Compile Include="LinearAlgebra\VectorDataAccessor.cs" />
+    <Compile Include="LinearAlgebra\VectorInitialization.cs" />
     <Compile Include="Properties\AssemblyInfo.cs" />
   </ItemGroup>
   <ItemGroup>
@@ -85,6 +105,12 @@
       <Install>true</Install>
     </BootstrapperPackage>
   </ItemGroup>
+  <ItemGroup>
+    <ProjectReference Include="..\Numerics\Numerics.csproj">
+      <Project>{B7CAE5F4-A23F-4438-B5BE-41226618B695}</Project>
+      <Name>Numerics</Name>
+    </ProjectReference>
+  </ItemGroup>
   <Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets" />
   <!-- To modify your build process, add your task inside one of the targets below and uncomment it. 
        Other similar extension points exist, see Microsoft.Common.targets.

src/Examples/LinearAlgebra/DirectSolvers.cs

@@ -0,0 +1,144 @@
+// <copyright file="DirectSolvers.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+// Copyright (c) 2009-2010 Math.NET
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+namespace Examples.LinearAlgebra
+{
+    using System;
+    using System.Globalization;
+    using MathNet.Numerics.LinearAlgebra.Double;
+    using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
+    /// <summary>
+    /// Direct solvers (using matrix decompositions)
+    /// </summary>
+    /// <seealso cref="http://en.wikipedia.org/wiki/Numerical_analysis#Direct_and_iterative_methods"/>
+    public class DirectSolvers : IExample
+    {
+        /// <summary>
+        /// Gets the name of this example
+        /// </summary>
+        public string Name
+        {
+            get
+            {
+                return "Direct solvers";
+            }
+        }
+
+        /// <summary>
+        /// Gets the description of this example
+        /// </summary>
+        public string Description
+        {
+            get
+            {
+                return "Solve linear equations using matrix decompositions";
+            }
+        }
+
+        /// <summary>
+        /// Run example
+        /// </summary>
+        public void Run()
+        {
+            // Format matrix output to console
+            var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
+            formatProvider.TextInfo.ListSeparator = " ";
+
+            // Solve next system of linear equations (Ax=b):
+            // 5*x + 2*y - 4*z = -7
+            // 3*x - 7*y + 6*z = 38
+            // 4*x + 1*y + 5*z = 43
+
+            // Create matrix "A" with coefficients 
+            var matrixA = new DenseMatrix(new[,] { { 5.00, 2.00, -4.00 }, { 3.00, -7.00, 6.00 }, { 4.00, 1.00, 5.00 } });
+            Console.WriteLine(@"Matrix 'A' with coefficients");
+            Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Create vector "b" with the constant terms.
+            var vectorB = new DenseVector(new[] { -7.0, 38.0, 43.0 });
+            Console.WriteLine(@"Vector 'b' with the constant terms");
+            Console.WriteLine(vectorB.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 1. Solve linear equations using LU decomposition
+            var resultX = matrixA.LU().Solve(vectorB);
+            Console.WriteLine(@"1. Solution using LU decomposition");
+            Console.WriteLine(resultX.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Solve linear equations using QR decomposition
+            resultX = matrixA.QR().Solve(vectorB);
+            Console.WriteLine(@"2. Solution using QR decomposition");
+            Console.WriteLine(resultX.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 3. Solve linear equations using SVD decomposition
+            matrixA.Svd(true).Solve(vectorB, resultX);
+            Console.WriteLine(@"3. Solution using SVD decomposition");
+            Console.WriteLine(resultX.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 4. Solve linear equations using Gram-Shmidt decomposition
+            matrixA.GramSchmidt().Solve(vectorB, resultX);
+            Console.WriteLine(@"4. Solution using Gram-Shmidt decomposition");
+            Console.WriteLine(resultX.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 5. Verify result. Multiply coefficient matrix "A" by result vector "x"
+            var reconstructVecorB = matrixA * resultX;
+            Console.WriteLine(@"5. Multiply coefficient matrix 'A' by result vector 'x'");
+            Console.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // To use Cholesky or Eigenvalue decomposition coefficient matrix must be 
+            // symmetric (for Evd and Cholesky) and positive definite (for Cholesky)
+            // Multipy matrix "A" by its transpose - the result will be symmetric and positive definite matrix
+            var newMatrixA = matrixA.TransposeAndMultiply(matrixA);
+            Console.WriteLine(@"Symmetric positive definite matrix");
+            Console.WriteLine(newMatrixA.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 6. Solve linear equations using Cholesky decomposition
+            newMatrixA.Cholesky().Solve(vectorB, resultX);
+            Console.WriteLine(@"6. Solution using Cholesky decomposition");
+            Console.WriteLine(resultX.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 7. Solve linear equations using eigen value decomposition
+            newMatrixA.Evd().Solve(vectorB, resultX);
+            Console.WriteLine(@"7. Solution using eigen value decomposition");
+            Console.WriteLine(resultX.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 8. Verify result. Multiply new coefficient matrix "A" by result vector "x"
+            reconstructVecorB = newMatrixA * resultX;
+            Console.WriteLine(@"8. Multiply new coefficient matrix 'A' by result vector 'x'");
+            Console.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+        }
+    }
+}

src/Examples/LinearAlgebra/Factorization/Cholesky.cs

@@ -0,0 +1,105 @@
+// <copyright file="Cholesky.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+// Copyright (c) 2009-2010 Math.NET
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace Examples.LinearAlgebra.Factorization
+{
+    using System;
+    using System.Globalization;
+    using MathNet.Numerics.LinearAlgebra.Double;
+    using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
+    /// <summary>
+    /// Cholesky factorization example. For a symmetric, positive definite matrix A, the Cholesky factorization
+    /// is an lower triangular matrix L so that A = L*L'
+    /// </summary>
+    /// <seealso cref="http://reference.wolfram.com/mathematica/ref/CholeskyDecomposition.html"/>
+    public class Cholesky : IExample
+    {
+        /// <summary>
+        /// Gets the name of this example
+        /// </summary>
+        public string Name
+        {
+            get
+            {
+                return "Cholesky factorization";
+            }
+        }
+
+        /// <summary>
+        /// Gets the description of this example
+        /// </summary>
+        public string Description
+        {
+            get
+            {
+                return "Perform the Cholesky factorization to the appropriate class";
+            }
+        }
+
+        /// <summary>
+        /// Run example
+        /// </summary>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Cholesky_decomposition">Cholesky decomposition</seealso>
+        public void Run()
+        {
+            // Format matrix output to console
+            var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
+            formatProvider.TextInfo.ListSeparator = " ";
+
+            // Create square, symmetric, positive definite matrix
+            var matrix = new DenseMatrix(new[,] { { 2.0, 1.0 }, { 1.0, 2.0 } });
+            Console.WriteLine(@"Initial square, symmetric, positive definite matrix");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Perform Cholesky decomposition
+            var cholesky = matrix.Cholesky();
+            Console.WriteLine(@"Perform Cholesky decomposition");
+
+            // 1. Lower triangular form of the Cholesky matrix
+            Console.WriteLine(@"1. Lower triangular form of the Cholesky matrix");
+            Console.WriteLine(cholesky.Factor.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Reconstruct initial matrix: A = L * LT
+            var reconstruct = cholesky.Factor * cholesky.Factor.Transpose();
+            Console.WriteLine(@"2. Reconstruct initial matrix: A = L*LT");
+            Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 3. Get determinant of the matrix
+            Console.WriteLine(@"3. Determinant of the matrix");
+            Console.WriteLine(cholesky.Determinant);
+            Console.WriteLine();
+
+            // 4. Get log determinant of the matrix
+            Console.WriteLine(@"4. Log determinant of the matrix");
+            Console.WriteLine(cholesky.DeterminantLn);
+            Console.WriteLine();
+        }
+    }
+}

src/Examples/LinearAlgebra/Factorization/Evd.cs

@@ -0,0 +1,188 @@
+// <copyright file="Evd.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+// Copyright (c) 2009-2010 Math.NET
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace Examples.LinearAlgebra.Factorization
+{
+    using System;
+    using System.Globalization;
+    using MathNet.Numerics.LinearAlgebra.Double;
+    using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
+    /// <summary>
+    /// EVD factorization example. If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is
+    /// diagonal and the eigenvector matrix V is orthogonal. I.e. A = V*D*V' and V*VT=I.
+    /// If A is not symmetric, then the eigenvalue matrix D is block diagonal
+    /// with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
+    /// lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda].  The
+    /// columns of V represent the eigenvectors in the sense thatA * V = V * D. 
+    /// The matrix V may be badly conditioned, or even singular, so the validity of the equation
+    /// A = V*D*Inverse(V) depends upon V.Condition()
+    /// </summary>
+    /// <seealso cref="http://reference.wolfram.com/mathematica/ref/Norm.html"/>
+    public class Evd : IExample
+    {
+         /// <summary>
+        /// Gets the name of this example
+        /// </summary>
+        public string Name
+        {
+            get
+            {
+                return "Evd factorization";
+            }
+        }
+
+        /// <summary>
+        /// Gets the description of this example
+        /// </summary>
+        public string Description
+        {
+            get
+            {
+                return "Perform the Evd factorization: eigenvalues and eigenvectors calculation";
+            }
+        }
+
+        /// <summary>
+        /// Run example
+        /// </summary>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Eigenvalue,_eigenvector_and_eigenspace">EVD decomposition</seealso>
+        public void Run()
+        {
+            // Format matrix output to console
+            var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
+            formatProvider.TextInfo.ListSeparator = " ";
+
+            // Create square symmetric matrix
+            var matrix = new DenseMatrix(new[,] { { 1.0, 2.0, 3.0 }, { 2.0, 1.0, 4.0 }, { 3.0, 4.0, 1.0 } });
+            Console.WriteLine(@"Initial square symmetric matrix");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Perform eigenvalue decomposition of symmetric matrix
+            var evd = matrix.Evd();
+            Console.WriteLine(@"Perform eigenvalue decomposition of symmetric matrix");
+
+            // 1. Eigen vectors
+            Console.WriteLine(@"1. Eigen vectors");
+            Console.WriteLine(evd.EigenVectors().ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Eigen values as a complex vector
+            Console.WriteLine(@"2. Eigen values as a complex vector");
+            Console.WriteLine(evd.EigenValues().ToString("N", formatProvider));
+            Console.WriteLine();
+
+            // 3. Eigen values as the block diagonal matrix
+            Console.WriteLine(@"3. Eigen values as the block diagonal matrix");
+            Console.WriteLine(evd.D().ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 4. Multiply V by its transpose VT
+            var identity = evd.EigenVectors().TransposeAndMultiply(evd.EigenVectors());
+            Console.WriteLine(@"4. Multiply V by its transpose VT: V*VT = I");
+            Console.WriteLine(identity.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 5. Reconstruct initial matrix: A = V*D*V'
+            var reconstruct = evd.EigenVectors() * evd.D() * evd.EigenVectors().Transpose();
+            Console.WriteLine(@"5. Reconstruct initial matrix: A = V*D*V'");
+            Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 6. Determinant of the matrix
+            Console.WriteLine(@"6. Determinant of the matrix");
+            Console.WriteLine(evd.Determinant);
+            Console.WriteLine();
+
+            // 7. Rank of the matrix
+            Console.WriteLine(@"7. Rank of the matrix");
+            Console.WriteLine(evd.Rank);
+            Console.WriteLine();
+
+            // Fill matrix by random values
+            var rnd = new Random(1);
+            for (var i = 0; i < matrix.RowCount; i++)
+            {
+                for (var j = 0; j < matrix.ColumnCount; j++)
+                {
+                    matrix[i, j] = rnd.NextDouble();
+                }
+            }
+
+            Console.WriteLine(@"Fill matrix by random values");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Perform eigenvalue decomposition of non-symmetric matrix
+            evd = matrix.Evd();
+            Console.WriteLine(@"Perform eigenvalue decomposition of non-symmetric matrix");
+
+            // 8. Eigen vectors
+            Console.WriteLine(@"8. Eigen vectors");
+            Console.WriteLine(evd.EigenVectors().ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 9. Eigen values as a complex vector
+            Console.WriteLine(@"9. Eigen values as a complex vector");
+            Console.WriteLine(evd.EigenValues().ToString("N", formatProvider));
+            Console.WriteLine();
+
+            // 10. Eigen values as the block diagonal matrix
+            Console.WriteLine(@"10. Eigen values as the block diagonal matrix");
+            Console.WriteLine(evd.D().ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 11. Multiply A * V
+            var av = matrix * evd.EigenVectors();
+            Console.WriteLine(@"11. Multiply A * V");
+            Console.WriteLine(av.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 12. Multiply V * D
+            var vd = evd.EigenVectors() * evd.D();
+            Console.WriteLine(@"12. Multiply V * D");
+            Console.WriteLine(vd.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 13. Reconstruct non-symmetriv matrix A = V * D * Vinverse
+            reconstruct = evd.EigenVectors() * evd.D() * evd.EigenVectors().Inverse();
+            Console.WriteLine(@"13. Reconstruct non-symmetriv matrix A = V * D * Vinverse");
+            Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 14. Determinant of the matrix
+            Console.WriteLine(@"14. Determinant of the matrix");
+            Console.WriteLine(evd.Determinant);
+            Console.WriteLine();
+
+            // 15. Rank of the matrix
+            Console.WriteLine(@"15. Rank of the matrix");
+            Console.WriteLine(evd.Rank);
+            Console.WriteLine();
+        }
+    }
+}

src/Examples/LinearAlgebra/Factorization/LU.cs

@@ -0,0 +1,135 @@
+// <copyright file="LU.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+// Copyright (c) 2009-2010 Math.NET
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace Examples.LinearAlgebra.Factorization
+{
+    using System;
+    using System.Globalization;
+    using MathNet.Numerics.LinearAlgebra.Double;
+    using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
+    /// <summary>
+    /// LU factorization example. For a matrix A, the LU factorization is a pair of lower triangular matrix L and
+    /// upper triangular matrix U so that A = L*U.
+    /// In the Math.Net implementation we also store a set of pivot elements for increased 
+    /// numerical stability. The pivot elements encode a permutation matrix P such that P*A = L*U
+    /// </summary>
+    /// <seealso cref="http://reference.wolfram.com/mathematica/ref/LUDecomposition.html"/>
+    public class LU : IExample
+    {
+        /// <summary>
+        /// Gets the name of this example
+        /// </summary>
+        public string Name
+        {
+            get
+            {
+                return "LU factorization";
+            }
+        }
+
+        /// <summary>
+        /// Gets the description of this example
+        /// </summary>
+        public string Description
+        {
+            get
+            {
+                return "Perform the LU factorization to the appropriate class";
+            }
+        }
+
+        /// <summary>
+        /// Run example
+        /// </summary>
+        /// <seealso cref="http://en.wikipedia.org/wiki/LU_decomposition">LU decomposition</seealso>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Invertible_matrix">Invertible matrix</seealso>
+        public void Run()
+        {
+            // Format matrix output to console
+            var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
+            formatProvider.TextInfo.ListSeparator = " ";
+
+            // Create square matrix
+            var matrix = new DenseMatrix(new[,] { { 1.0, 2.0 }, { 3.0, 4.0 } });
+            Console.WriteLine(@"Initial square matrix");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Perform LU decomposition
+            var lu = matrix.LU();
+            Console.WriteLine(@"Perform LU decomposition");
+
+            // 1. Lower triangular factor
+            Console.WriteLine(@"1. Lower triangular factor");
+            Console.WriteLine(lu.L.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Upper triangular factor
+            Console.WriteLine(@"2. Upper triangular factor");
+            Console.WriteLine(lu.U.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 3. Permutations applied to LU factorization
+            Console.WriteLine(@"3. Permutations applied to LU factorization");
+            for (var i = 0; i < lu.P.Dimension; i++)
+            {
+                if (lu.P[i] > i)
+                {
+                    Console.WriteLine(@"Row {0} permuted with row {1}", lu.P[i], i);
+                }
+            }
+
+            Console.WriteLine();
+
+            // 4. Reconstruct initial matrix: PA = L * U
+            var reconstruct = lu.L * lu.U;
+
+            // The rows of the reconstructed matrix should be permuted to get the initial matrix
+            reconstruct.PermuteRows(lu.P.Inverse());
+            Console.WriteLine(@"4. Reconstruct initial matrix: PA = L*U");
+            Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 5. Get the determinant of the matrix
+            Console.WriteLine(@"5. Determinant of the matrix");
+            Console.WriteLine(lu.Determinant);
+            Console.WriteLine();
+
+            // 6. Get the inverse of the matrix
+            var matrixInverse = lu.Inverse();
+            Console.WriteLine(@"6. Inverse of the matrix");
+            Console.WriteLine(matrixInverse.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 7. Matrix multiplied by its inverse 
+            var identity = matrix * matrixInverse;
+            Console.WriteLine(@"7. Matrix multiplied by its inverse ");
+            Console.WriteLine(identity.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+        }
+    }
+}

src/Examples/LinearAlgebra/Factorization/QR.cs

@@ -0,0 +1,132 @@
+// <copyright file="QR.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+// Copyright (c) 2009-2010 Math.NET
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace Examples.LinearAlgebra.Factorization
+{
+    using System;
+    using System.Globalization;
+    using MathNet.Numerics.LinearAlgebra.Double;
+    using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
+    /// <summary>
+    /// QR factorization example. Any real square matrix A (m x n) may be decomposed as A = QR where Q is an orthogonal matrix (m x m)
+    /// (its columns are orthogonal unit vectors meaning QTQ = I) and R (m x n) is an upper triangular matrix 
+    /// (also called right triangular matrix).
+    /// In this example two methods for actually computing the QR decomposition presented: by means of the Gram–Schmidt process and Householder transformations.
+    /// </summary>
+    /// <seealso cref="http://reference.wolfram.com/mathematica/ref/QRDecomposition.html"/>
+    public class QR : IExample
+    {
+        /// <summary>
+        /// Gets the name of this example
+        /// </summary>
+        public string Name
+        {
+            get
+            {
+                return "QR factorization";
+            }
+        }
+
+        /// <summary>
+        /// Gets the description of this example
+        /// </summary>
+        public string Description
+        {
+            get
+            {
+                return "Perform the QR factorization by means of the Gram–Schmidt process and Householder transformations";
+            }
+        }
+
+        /// <summary>
+        /// Run example
+        /// </summary>
+        /// <seealso cref="http://en.wikipedia.org/wiki/QR_decomposition">QR decomposition</seealso>
+        public void Run()
+        {
+            // Format matrix output to console
+            var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
+            formatProvider.TextInfo.ListSeparator = " ";
+
+            // Create 3 x 2 matrix
+            var matrix = new DenseMatrix(new[,] { { 1.0, 2.0 }, { 3.0, 4.0 }, { 5.0, 6.0 } });
+            Console.WriteLine(@"Initial 3x2 matrix");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Perform QR decomposition (Householder transformations)
+            var qr = matrix.QR();
+            Console.WriteLine(@"QR decomposition (Householder transformations)");
+
+            // 1. Orthogonal Q matrix
+            Console.WriteLine(@"1. Orthogonal Q matrix");
+            Console.WriteLine(qr.Q.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Multiply Q matrix by its transpose gives identity matrix
+            Console.WriteLine(@"2. Multiply Q matrix by its transpose gives identity matrix");
+            Console.WriteLine(qr.Q.TransposeAndMultiply(qr.Q).ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 3. Upper triangular factor R
+            Console.WriteLine(@"3. Upper triangular factor R");
+            Console.WriteLine(qr.R.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 4. Reconstruct initial matrix: A = Q * R
+            var reconstruct = qr.Q * qr.R;
+            Console.WriteLine(@"4. Reconstruct initial matrix: A = Q*R");
+            Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Perform QR decomposition (Gram–Schmidt process)
+            qr = matrix.GramSchmidt();
+            Console.WriteLine(@"QR decomposition (Gram–Schmidt process)");
+
+            // 5. Orthogonal Q matrix
+            Console.WriteLine(@"5. Orthogonal Q matrix");
+            Console.WriteLine(qr.Q.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 6. Multiply Q matrix by its transpose gives identity matrix
+            Console.WriteLine(@"6. Multiply Q matrix by its transpose gives identity matrix");
+            Console.WriteLine((qr.Q.Transpose() * qr.Q).ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 7. Upper triangular factor R
+            Console.WriteLine(@"7. Upper triangular factor R");
+            Console.WriteLine(qr.R.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+            
+            // 8. Reconstruct initial matrix: A = Q * R
+            reconstruct = qr.Q * qr.R;
+            Console.WriteLine(@"8. Reconstruct initial matrix: A = Q*R");
+            Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+        }
+    }
+}

src/Examples/LinearAlgebra/Factorization/Svd.cs

@@ -0,0 +1,186 @@
+// <copyright file="Svd.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+// Copyright (c) 2009-2010 Math.NET
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace Examples.LinearAlgebra.Factorization
+{
+    using System;
+    using System.Globalization;
+    using MathNet.Numerics.LinearAlgebra.Double;
+    using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
+    /// <summary>
+    /// SVD factorization example. Suppose M is an m-by-n matrix whose entries are real numbers. 
+    /// Then there exists a factorization of the form M = UΣVT where:
+    /// - U is an m-by-m unitary matrix;
+    /// - Σ is m-by-n diagonal matrix with nonnegative real numbers on the diagonal;
+    /// - VT denotes transpose of V, an n-by-n unitary matrix; 
+    /// Such a factorization is called a singular-value decomposition of M. A common convention is to order the diagonal 
+    /// entries Σ(i,i) in descending order. In this case, the diagonal matrix Σ is uniquely determined 
+    /// by M (though the matrices U and V are not). The diagonal entries of Σ are known as the singular values of M.
+    /// </summary>
+    /// <seealso cref="http://reference.wolfram.com/mathematica/ref/SingularValueDecomposition.html"/>
+    public class Svd : IExample
+    {
+        /// <summary>
+        /// Gets the name of this example
+        /// </summary>
+        public string Name
+        {
+            get
+            {
+                return "Svd factorization";
+            }
+        }
+
+        /// <summary>
+        /// Gets the description of this example
+        /// </summary>
+        public string Description
+        {
+            get
+            {
+                return "Perform the Svd factorization";
+            }
+        }
+
+        /// <summary>
+        /// Run example
+        /// </summary>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Singular_value_decomposition">SVD decomposition</seealso>
+        public void Run()
+        {
+            // Format matrix output to console
+            var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
+            formatProvider.TextInfo.ListSeparator = " ";
+
+            // Create square matrix
+            var matrix = new DenseMatrix(new[,] { { 4.0, 1.0 }, { 3.0, 2.0 } });
+            Console.WriteLine(@"Initial square matrix");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Perform full SVD decomposition
+            var svd = matrix.Svd(true);
+            Console.WriteLine(@"Perform full SVD decomposition");
+
+            // 1. Left singular vectors
+            Console.WriteLine(@"1. Left singular vectors");
+            Console.WriteLine(svd.U().ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Singular values as vector
+            Console.WriteLine(@"2. Singular values as vector");
+            Console.WriteLine(svd.S().ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 3. Singular values as diagonal matrix
+            Console.WriteLine(@"3. Singular values as diagonal matrix");
+            Console.WriteLine(svd.W().ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 4. Right singular vectors
+            Console.WriteLine(@"4. Right singular vectors");
+            Console.WriteLine(svd.VT().ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 5. Multiply U matrix by its transpose
+            var identinty = svd.U() * svd.U().Transpose();
+            Console.WriteLine(@"5. Multiply U matrix by its transpose");
+            Console.WriteLine(identinty.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 6. Multiply V matrix by its transpose
+            identinty = svd.VT().TransposeAndMultiply(svd.VT());
+            Console.WriteLine(@"6. Multiply V matrix by its transpose");
+            Console.WriteLine(identinty.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 7. Reconstruct initial matrix: A = U*Σ*VT
+            var reconstruct = svd.U() * svd.W() * svd.VT();
+            Console.WriteLine(@"7. Reconstruct initial matrix: A = U*S*VT");
+            Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 8. Condition Number of the matrix
+            Console.WriteLine(@"8. Condition Number of the matrix");
+            Console.WriteLine(svd.ConditionNumber);
+            Console.WriteLine();
+
+            // 9. Determinant of the matrix
+            Console.WriteLine(@"9. Determinant of the matrix");
+            Console.WriteLine(svd.Determinant);
+            Console.WriteLine();
+
+            // 10. 2-norm of the matrix
+            Console.WriteLine(@"10. 2-norm of the matrix");
+            Console.WriteLine(svd.Norm2);
+            Console.WriteLine();
+
+            // 11. Rank of the matrix
+            Console.WriteLine(@"11. Rank of the matrix");
+            Console.WriteLine(svd.Rank);
+            Console.WriteLine();
+
+            // Perform partial SVD decomposition, without computing the singular U and VT vectors
+            svd = matrix.Svd(false);
+            Console.WriteLine(@"Perform partial SVD decomposition, without computing the singular U and VT vectors");
+
+            // 12. Singular values as vector
+            Console.WriteLine(@"12. Singular values as vector");
+            Console.WriteLine(svd.S().ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 13. Singular values as diagonal matrix
+            Console.WriteLine(@"13. Singular values as diagonal matrix");
+            Console.WriteLine(svd.W().ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 14. Access to left singular vectors when partial SVD decomposition was performed
+            try
+            {
+                Console.WriteLine(@"14. Access to left singular vectors when partial SVD decomposition was performed");
+                Console.WriteLine(svd.U().ToString("#0.00\t", formatProvider));
+            }
+            catch (Exception ex)
+            {
+                Console.WriteLine(ex.Message);
+                Console.WriteLine();
+            }
+
+            // 15. Access to right singular vectors when partial SVD decomposition was performed
+            try
+            {
+                Console.WriteLine(@"15. Access to right singular vectors when partial SVD decomposition was performed");
+                Console.WriteLine(svd.VT().ToString("#0.00\t", formatProvider));
+            }
+            catch (Exception ex)
+            {
+                Console.WriteLine(ex.Message);
+                Console.WriteLine();
+            }
+        }
+    }
+}

src/Examples/LinearAlgebra/MatrixArithmeticOperations.cs

@@ -0,0 +1,246 @@
+// <copyright file="MatrixArithmeticOperations.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+// Copyright (c) 2009-2010 Math.NET
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace Examples.LinearAlgebra
+{
+    using System;
+    using System.Globalization;
+    using MathNet.Numerics.LinearAlgebra.Double;
+
+    /// <summary>
+    /// Basic matrix arithmetic operations as "+", "-", "*", "/"
+    /// </summary>
+    /// <seealso cref="http://reference.wolfram.com/mathematica/tutorial/VectorsAndMatrices.html"/>
+    public class MatrixArithmeticOperations : IExample
+    {
+        /// <summary>
+        /// Gets the name of this example
+        /// </summary>
+        public string Name
+        {
+            get
+            {
+                return "Matrix Arithmetics";
+            }
+        }
+
+        /// <summary>
+        /// Gets the description of this example
+        /// </summary>
+        public string Description
+        {
+            get
+            {
+                return "Basic operations between matrix/matrix and matrix/vecor";
+            }
+        }
+
+        /// <summary>
+        /// Run example
+        /// </summary>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Matrix_multiplication#Scalar_multiplication">Multiply matrix by scalar</seealso>
+        /// <seealso cref="http://reference.wolfram.com/mathematica/tutorial/MultiplyingVectorsAndMatrices.html">Multiply matrix by vector</seealso>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Matrix_multiplication#Matrix_product">Multiply matrix by matrix</seealso>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Matrix_multiplication#Hadamard_product">Pointwise multiplie matrix with another matrix</seealso>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Matrix_%28mathematics%29#Basic_operations">Addition and subtraction</seealso>
+        public void Run()
+        {
+            // Initialize IFormatProvider to print matrix/vector data 
+            var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
+            formatProvider.TextInfo.ListSeparator = " ";
+
+            // Create matrix "A"
+            var matrixA = new DenseMatrix(new[,] { { 1.0, 2.0, 3.0 }, { 4.0, 5.0, 6.0 }, { 7.0, 8.0, 9.0 } });
+            Console.WriteLine(@"Matrix A");
+            Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Create matrix "B"
+            var matrixB = new DenseMatrix(new[,] { { 1.0, 3.0, 5.0 }, { 2.0, 4.0, 6.0 }, { 3.0, 5.0, 7.0 } });
+            Console.WriteLine(@"Matrix B");
+            Console.WriteLine(matrixB.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Multiply matrix by scalar
+            // 1. Using operator "*"
+            var resultM = 3.0 * matrixA;
+            Console.WriteLine(@"Multiply matrix by scalar using operator *. (result = 3.0 * A)");
+            Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Using Multiply method and getting result into different matrix instance
+            resultM = matrixA.Multiply(3.0);
+            Console.WriteLine(@"Multiply matrix by scalar using method Multiply. (result = A.Multiply(3.0))");
+            Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 3. Using Multiply method and updating matrix itself
+            matrixA.Multiply(3.0, matrixA);
+            Console.WriteLine(@"Multiply matrix by scalar using method Multiply. (A.Multiply(3.0, A))");
+            Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Multiply matrix by vector (right-multiply)
+            var vector = new DenseVector(new[] { 1.0, 2.0, 3.0 });
+            Console.WriteLine(@"Vector");
+            Console.WriteLine(vector.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 1. Using operator "*"
+            var resultV = matrixA * vector;
+            Console.WriteLine(@"Multiply matrix by vector using operator *. (result = A * vec)");
+            Console.WriteLine(resultV.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Using Multiply method and getting result into different vector instance
+            resultV = matrixA.Multiply(vector);
+            Console.WriteLine(@"Multiply matrix by vector using method Multiply. (result = A.Multiply(vec))");
+            Console.WriteLine(resultV.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 3. Using Multiply method and updating vector itself
+            matrixA.Multiply(vector, vector);
+            Console.WriteLine(@"Multiply matrix by vector using method Multiply. (A.Multiply(vec, vec))");
+            Console.WriteLine(vector.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Multiply vector by matrix (left-multiply)
+            // 1. Using operator "*"
+            resultV = vector * matrixA;
+            Console.WriteLine(@"Multiply vector by matrix using operator *. (result = vec * A)");
+            Console.WriteLine(resultV.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Using LeftMultiply method and getting result into different vector instance
+            resultV = matrixA.LeftMultiply(vector);
+            Console.WriteLine(@"Multiply vector by matrix using method LeftMultiply. (result = A.LeftMultiply(vec))");
+            Console.WriteLine(resultV.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 3. Using LeftMultiply method and updating vector itself
+            matrixA.LeftMultiply(vector, vector);
+            Console.WriteLine(@"Multiply vector by matrix using method LeftMultiply. (A.LeftMultiply(vec, vec))");
+            Console.WriteLine(vector.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Multiply matrix by matrix
+            // 1. Using operator "*"
+            resultM = matrixA * matrixB;
+            Console.WriteLine(@"Multiply matrix by matrix using operator *. (result = A * B)");
+            Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Using Multiply method and getting result into different matrix instance
+            resultM = matrixA.Multiply(matrixB);
+            Console.WriteLine(@"Multiply matrix by matrix using method Multiply. (result = A.Multiply(B))");
+            Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 3. Using Multiply method and updating matrix itself
+            matrixA.Multiply(matrixB, matrixA);
+            Console.WriteLine(@"Multiply matrix by matrix using method Multiply. (A.Multiply(B, A))");
+            Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Pointwise multiplie matrix with another matrix
+            // 1. Using PointwiseMultiply method and getting result into different matrix instance
+            resultM = matrixA.PointwiseMultiply(matrixB);
+            Console.WriteLine(@"Pointwise multiplie matrix with another matrix using method PointwiseMultiply. (result = A.PointwiseMultiply(B))");
+            Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Using PointwiseMultiply method and updating matrix itself
+            matrixA.PointwiseMultiply(matrixB, matrixA);
+            Console.WriteLine(@"Pointwise multiplie matrix with another matrix using method PointwiseMultiply. (A.PointwiseMultiply(B, A))");
+            Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Pointwise divide matrix with another matrix
+            // 1. Using PointwiseDivide method and getting result into different matrix instance
+            resultM = matrixA.PointwiseDivide(matrixB);
+            Console.WriteLine(@"Pointwise divide matrix with another matrix using method PointwiseDivide. (result = A.PointwiseDivide(B))");
+            Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Using PointwiseDivide method and updating matrix itself
+            matrixA.PointwiseDivide(matrixB, matrixA);
+            Console.WriteLine(@"Pointwise divide matrix with another matrix using method PointwiseDivide. (A.PointwiseDivide(B, A))");
+            Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Addition
+            // 1. Using operator "+"
+            resultM = matrixA + matrixB;
+            Console.WriteLine(@"Add matrices using operator +. (result = A + B)");
+            Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Using Add method and getting result into different matrix instance
+            resultM = matrixA.Add(matrixB);
+            Console.WriteLine(@"Add matrices using method Add. (result = A.Add(B))");
+            Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 3. Using Add method and updating matrix itself
+            matrixA.Add(matrixB, matrixA);
+            Console.WriteLine(@"Add matrices using method Add. (A.Add(B, A))");
+            Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Subtraction
+            // 1. Using operator "-"
+            resultM = matrixA - matrixB;
+            Console.WriteLine(@"Subtract matrices using operator -. (result = A - B)");
+            Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Using Subtract method and getting result into different matrix instance
+            resultM = matrixA.Subtract(matrixB);
+            Console.WriteLine(@"Subtract matrices using method Subtract. (result = A.Subtract(B))");
+            Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 3. Using Subtract method and updating matrix itself
+            matrixA.Subtract(matrixB, matrixA);
+            Console.WriteLine(@"Subtract matrices using method Subtract. (A.Subtract(B, A))");
+            Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Divide by scalar
+            // 1. Using Divide method and getting result into different matrix instance
+            resultM = matrixA.Divide(3.0);
+            Console.WriteLine(@"Divide matrix by scalar using method Divide. (result = A.Divide(3.0))");
+            Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Using Divide method and updating matrix itself
+            matrixA.Divide(3.0, matrixA);
+            Console.WriteLine(@"Divide matrix by scalar using method Divide. (A.Divide(3.0, A))");
+            Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+        }
+    }
+}

src/Examples/LinearAlgebra/MatrixDataAccessor.cs

@@ -0,0 +1,208 @@
+// <copyright file="MatrixDataAccessor.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+// Copyright (c) 2009-2010 Math.NET
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace Examples.LinearAlgebra
+{
+    using System;
+    using System.Globalization;
+    using MathNet.Numerics.LinearAlgebra.Double;
+
+    /// <summary>
+    /// Matrix data access, copying and conversion examples
+    /// </summary>
+    public class MatrixDataAccessor
+    {
+        /// <summary>
+        /// Gets the name of this example
+        /// </summary>
+        public string Name
+        {
+            get
+            {
+                return "Matrix data access, copying and conversion";
+            }
+        }
+
+        /// <summary>
+        /// Gets the description of this example
+        /// </summary>
+        public string Description
+        {
+            get
+            {
+                return "Examples of setting/getting values of a matrix, copying and conversion matrix into another matrix";
+            }
+        }
+
+        /// <summary>
+        /// Run example
+        /// </summary>
+        public void Run()
+        {
+            // Format vector output to console
+            var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
+            formatProvider.TextInfo.ListSeparator = " ";
+
+            // Create new empty square matrix
+            var matrix = new DenseMatrix(10);
+            Console.WriteLine(@"Empty matrix");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 1. Fill matrix by data using indexer []
+            var k = 0;
+            for (var i = 0; i < matrix.RowCount; i++)
+            {
+                for (var j = 0; j < matrix.ColumnCount; j++)
+                {
+                    matrix[i, j] = k++;
+                }
+            }
+
+            Console.WriteLine(@"1. Fill matrix by data using indexer []");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Fill matrix by data using At. The element is set without range checking.
+            for (var i = 0; i < matrix.RowCount; i++)
+            {
+                for (var j = 0; j < matrix.ColumnCount; j++)
+                {
+                    matrix.At(i, j, k--);
+                }
+            }
+
+            Console.WriteLine(@"2. Fill matrix by data using At");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 3. Clone matrix
+            var clone = matrix.Clone();
+            Console.WriteLine(@"3. Clone matrix");
+            Console.WriteLine(clone.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 4. Clear matrix
+            clone.Clear();
+            Console.WriteLine(@"4. Clear matrix");
+            Console.WriteLine(clone.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 5. Copy matrix into another matrix
+            matrix.CopyTo(clone);
+            Console.WriteLine(@"5. Copy matrix into another matrix");
+            Console.WriteLine(clone.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 6. Get submatrix into another matrix
+            var submatrix = matrix.SubMatrix(2, 2, 3, 3);
+            Console.WriteLine(@"6. Copy submatrix into another matrix");
+            Console.WriteLine(submatrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 7. Get part of the row as vector. In this example: get 4 elements from row 5 starting from column 3
+            var row = matrix.Row(5, 3, 4);
+            Console.WriteLine(@"7. Get part of the row as vector");
+            Console.WriteLine(row.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 8. Get part of the column as vector. In this example: get 3 elements from column 2 starting from row 6
+            var column = matrix.Column(2, 6, 3);
+            Console.WriteLine(@"8. Get part of the column as vector");
+            Console.WriteLine(column.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 9. Get columns using column enumerator. If you need all columns you may use ColumnEnumerator without parameters
+            Console.WriteLine(@"9. Get columns using column enumerator");
+            foreach (var keyValuePair in matrix.ColumnEnumerator(2, 4))
+            {
+                Console.WriteLine(@"Column {0}: {1}", keyValuePair.Key, keyValuePair.Value.ToString("#0.00\t", formatProvider));
+            }
+
+            Console.WriteLine();
+
+            // 10. Get rows using row enumerator. If you need all rows you may use RowEnumerator without parameters
+            Console.WriteLine(@"10. Get rows using row enumerator");
+            foreach (var keyValuePair in matrix.RowEnumerator(4, 3))
+            {
+                Console.WriteLine(@"Row {0}: {1}", keyValuePair.Key, keyValuePair.Value.ToString("#0.00\t", formatProvider));
+            }
+
+            Console.WriteLine();
+
+            // 11. Convert matrix into multidimensional array
+            var data = matrix.ToArray();
+            Console.WriteLine(@"11. Convert matrix into multidimensional array");
+            for (var i = 0; i < data.GetLongLength(0); i++)
+            {
+                for (var j = 0; j < data.GetLongLength(1); j++)
+                {
+                    Console.Write(data[i, j].ToString("#0.00\t"));
+                }
+
+                Console.WriteLine();
+            }
+
+            Console.WriteLine();
+
+            // 12. Convert matrix into row-wise array
+            var rowwise = matrix.ToRowWiseArray();
+            Console.WriteLine(@"12. Convert matrix into row-wise array");
+            for (var i = 0; i < matrix.RowCount; i++)
+            {
+                for (var j = 0; j < matrix.ColumnCount; j++)
+                {
+                    Console.Write(rowwise[(i * matrix.ColumnCount) + j].ToString("#0.00\t"));
+                }
+
+                Console.WriteLine();
+            }
+
+            Console.WriteLine();
+
+            // 13. Convert matrix into column-wise array
+            var columnise = matrix.ToColumnWiseArray();
+            Console.WriteLine(@"13. Convert matrix into column-wise array");
+            for (var i = 0; i < matrix.RowCount; i++)
+            {
+                for (var j = 0; j < matrix.ColumnCount; j++)
+                {
+                    Console.Write(columnise[(j * matrix.RowCount) + i].ToString("#0.00\t"));
+                }
+
+                Console.WriteLine();
+            }
+
+            Console.WriteLine();
+
+            // 14. Get matrix diagonal as vector
+            var diagonal = matrix.Diagonal();
+            Console.WriteLine(@"14. Get matrix diagonal as vector");
+            Console.WriteLine(diagonal.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+        }
+    }
+}

src/Examples/LinearAlgebra/MatrixInitialization.cs

@@ -0,0 +1,112 @@
+// <copyright file="MatrixInitialization.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+// Copyright (c) 2009-2010 Math.NET
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace Examples.LinearAlgebra
+{
+    using System;
+    using System.Globalization;
+    using MathNet.Numerics.LinearAlgebra.Double;
+
+    /// <summary>
+    /// Matrix initialization examples
+    /// </summary>
+    public class MatrixInitialization : IExample
+    {
+        /// <summary>
+        /// Gets the name of this example
+        /// </summary>
+        public string Name
+        {
+            get
+            {
+                return "Matrix initialization";
+            }
+        }
+
+        /// <summary>
+        /// Gets the description of this example
+        /// </summary>
+        public string Description
+        {
+            get
+            {
+                return "Examples of creating matrix instances";
+            }
+        }
+
+        /// <summary>
+        /// Run example
+        /// </summary>
+        public void Run()
+        {
+            // 1. Initialize a new instance of the matrix from a 2D array. This constructor will allocate a completely new memory block for storing the dense matrix.
+            var matrix1 = new DenseMatrix(new[,] { { 1.0, 2.0, 3.0 }, { 4.0, 5.0, 6.0 } });
+
+            // 2. Initialize a new instance of the empty square matrix with a given order.
+            var matrix2 = new DenseMatrix(3);
+
+            // 3. Initialize a new instance of the empty matrix with a given size.
+            var matrix3 = new DenseMatrix(2, 3);
+
+            // 4. Initialize a new instance of the matrix with all entries set to a particular value.
+            var matrix4 = new DenseMatrix(2, 3, 3.0);
+
+            // 4. Initialize a new instance of the matrix from a one dimensional array. This array should store the matrix in column-major order. 
+            var matrix5 = new DenseMatrix(2, 3, new[] { 1.0, 4.0, 2.0, 5.0, 3.0, 6.0 });
+
+            // 5. Initialize a square matrix with all zero's except for ones on the diagonal. Identity matrix (http://en.wikipedia.org/wiki/Identity_matrix).
+            var matrixI = DenseMatrix.Identity(5);
+
+            // Format matrix output to console
+            var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
+            formatProvider.TextInfo.ListSeparator = " ";
+
+            Console.WriteLine(@"Matrix 1");
+            Console.WriteLine(matrix1.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            Console.WriteLine(@"Matrix 2");
+            Console.WriteLine(matrix2.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            Console.WriteLine(@"Matrix 3");
+            Console.WriteLine(matrix3.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            Console.WriteLine(@"Matrix 4");
+            Console.WriteLine(matrix4.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            Console.WriteLine(@"Matrix 5");
+            Console.WriteLine(matrix5.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            Console.WriteLine(@"Identity matrix");
+            Console.WriteLine(matrixI.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+        }
+    }
+}

src/Examples/LinearAlgebra/MatrixNorms.cs

@@ -0,0 +1,129 @@
+// <copyright file="MatrixNorms.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+// Copyright (c) 2009-2010 Math.NET
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace Examples.LinearAlgebra
+{
+    using System;
+    using System.Globalization;
+    using MathNet.Numerics.LinearAlgebra.Double;
+
+    /// <summary>
+    /// Matrix norms 
+    /// </summary>
+    public class MatrixNorms : IExample
+    {
+        /// <summary>
+        /// Gets the name of this example
+        /// </summary>
+        public string Name
+        {
+            get
+            {
+                return "Matrix norms";
+            }
+        }
+
+        /// <summary>
+        /// Gets the description of this example
+        /// </summary>
+        public string Description
+        {
+            get
+            {
+                return "Examples of matrix norms: L1 norm, L2 norm, Frobenius norm and infinity norm";
+            }
+        }
+
+        /// <summary>
+        /// Run example
+        /// </summary>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Matrix_norm">Matrix norm</seealso>
+        public void Run()
+        {
+            // Format matrix output to console
+            var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
+            formatProvider.TextInfo.ListSeparator = " ";
+
+            // Create square matrix
+            var matrix = new DenseMatrix(new[,] { { 1.0, 2.0, 3.0 }, { 6.0, 5.0, 4.0 }, { 8.0, 9.0, 7.0 } });
+            Console.WriteLine(@"Initial square matrix");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 1. 1-norm of the matrix
+            Console.WriteLine(@"1. 1-norm of the matrix");
+            Console.WriteLine(matrix.L1Norm());
+            Console.WriteLine();
+
+            // 2. 2-norm of the matrix
+            Console.WriteLine(@"2. 2-norm of the matrix");
+            Console.WriteLine(matrix.L2Norm());
+            Console.WriteLine();
+
+            // 3. Frobenius norm of the matrix
+            Console.WriteLine(@"3. Frobenius norm of the matrix");
+            Console.WriteLine(matrix.FrobeniusNorm());
+            Console.WriteLine();
+
+            // 4. Infinity norm of the matrix
+            Console.WriteLine(@"4. Infinity norm of the matrix");
+            Console.WriteLine(matrix.InfinityNorm());
+            Console.WriteLine();
+
+            // 5. Normalize matrix columns
+            Console.WriteLine(@"5. Normalize matrix columns: before normalize");
+            foreach (var keyValuePair in matrix.ColumnEnumerator())
+            {
+                Console.WriteLine(@"Column {0} 2-nd norm is: {1}", keyValuePair.Key, keyValuePair.Value.Norm(2));
+            }
+
+            Console.WriteLine();
+            var normalized = matrix.NormalizeColumns(2);
+            Console.WriteLine(@"5. Normalize matrix columns: after normalize");
+            foreach (var keyValuePair in normalized.ColumnEnumerator())
+            {
+                Console.WriteLine(@"Column {0} 2-nd norm is: {1}", keyValuePair.Key, keyValuePair.Value.Norm(2));
+            }
+
+            Console.WriteLine();
+
+            // 6. Normalize matrix columns
+            Console.WriteLine(@"6. Normalize matrix rows: before normalize");
+            foreach (var keyValuePair in matrix.RowEnumerator())
+            {
+                Console.WriteLine(@"Row {0} 2-nd norm is: {1}", keyValuePair.Key, keyValuePair.Value.Norm(2));
+            }
+
+            Console.WriteLine();
+            normalized = matrix.NormalizeRows(2);
+            Console.WriteLine(@"6. Normalize matrix rows: after normalize");
+            foreach (var keyValuePair in normalized.RowEnumerator())
+            {
+                Console.WriteLine(@"Row {0} 2-nd norm is: {1}", keyValuePair.Key, keyValuePair.Value.Norm(2));
+            }
+        }
+    }
+}

src/Examples/LinearAlgebra/MatrixRowColumnOperations.cs

@@ -0,0 +1,173 @@
+// <copyright file="MatrixRowColumnOperations.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+// Copyright (c) 2009-2010 Math.NET
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace Examples.LinearAlgebra
+{
+    using System;
+    using System.Globalization;
+    using MathNet.Numerics;
+    using MathNet.Numerics.LinearAlgebra.Double;
+
+    /// <summary>
+    /// Matrix operations with rows and columns
+    /// </summary>
+    public class MatrixRowColumnOperations : IExample
+    {
+        /// <summary>
+        /// Gets the name of this example
+        /// </summary>
+        public string Name
+        {
+            get
+            {
+                return "Matrix row and column operations";
+            }
+        }
+
+        /// <summary>
+        /// Gets the description of this example
+        /// </summary>
+        public string Description
+        {
+            get
+            {
+                return "Examples of permuting, modifying, inserting columns and rows in a matrix";
+            }
+        }
+
+        /// <summary>
+        /// Run example
+        /// </summary>
+        public void Run()
+        {
+            // Format matrix output to console
+            var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
+            formatProvider.TextInfo.ListSeparator = " ";
+            
+            // Create square matrix
+            var matrix = new DenseMatrix(5);
+            var k = 0;
+            for (var i = 0; i < matrix.RowCount; i++)
+            {
+                for (var j = 0; j < matrix.ColumnCount; j++)
+                {
+                    matrix[i, j] = k++;
+                }
+            }
+
+            Console.WriteLine(@"Initial matrix");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Create vector
+            var vector = new DenseVector(new[] { 50.0, 51.0, 52.0, 53.0, 54.0 });
+            Console.WriteLine(@"Sample vector");
+            Console.WriteLine(vector.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 1. Insert new column
+            var result = matrix.InsertColumn(3, vector);
+            Console.WriteLine(@"1. Insert new column");
+            Console.WriteLine(result.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Insert new row
+            result = matrix.InsertRow(3, vector);
+            Console.WriteLine(@"2. Insert new row");
+            Console.WriteLine(result.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 3. Set column values
+            matrix.SetColumn(2, (Vector)vector);
+            Console.WriteLine(@"3. Set column values");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 4. Set row values. 
+            matrix.SetRow(3, (double[])vector);
+            Console.WriteLine(@"4. Set row values");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 5. Set diagonal values. SetRow/SetColumn/SetDiagonal accepts Vector and double[] as input parameter
+            matrix.SetDiagonal(new[] { 5.0, 4.0, 3.0, 2.0, 1.0 });
+            Console.WriteLine(@"5. Set diagonal values");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 6. Set submatrix values
+            matrix.SetSubMatrix(1, 3, 1, 3, DenseMatrix.Identity(3));
+            Console.WriteLine(@"6. Set submatrix values");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Permutations. 
+            // Initialize a new instance of the Permutation class. An array represents where each integer is permuted too: 
+            // indices[i] represents that integer "i" is permuted to location indices[i]
+            var permutations = new Permutation(new[] { 0, 1, 3, 2, 4 });
+            
+            // 7. Permute rows 3 and 4
+            matrix.PermuteRows(permutations);
+            Console.WriteLine(@"7. Permute rows 3 and 4");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 8. Permute columns 1 and 2, 3 and 5
+            permutations = new Permutation(new[] { 1, 0, 4, 3, 2 });
+            matrix.PermuteColumns(permutations);
+            Console.WriteLine(@"8. Permute columns 1 and 2, 3 and 5");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 9. Concatenate the matrix with the given matrix
+            var append = matrix.Append(matrix);
+
+            // Concatenate into result matrix
+            matrix.Append(matrix, append);
+            Console.WriteLine(@"9. Append matrix to matrix");
+            Console.WriteLine(append.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+             // 10. Stack the matrix on top of the given matrix matrix
+            var stack = matrix.Stack(matrix);
+
+            // Stack into result matrix
+            matrix.Stack(matrix, stack);
+            Console.WriteLine(@"10. Stack the matrix on top of the given matrix matrix");
+            Console.WriteLine(stack.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 11. Diagonally stack the matrix on top of the given matrix matrix
+            var diagoinalStack = matrix.DiagonalStack(matrix);
+
+            // Diagonally stack into result matrix
+            matrix.DiagonalStack(matrix, diagoinalStack);
+            Console.WriteLine(@"11. Diagonally stack the matrix on top of the given matrix matrix");
+            Console.WriteLine(diagoinalStack.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+        }
+    }
+}

src/Examples/LinearAlgebra/MatrixSpecialNumbers.cs

@@ -0,0 +1,112 @@
+// <copyright file="MatrixSpecialNumbers.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+// Copyright (c) 2009-2010 Math.NET
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace Examples.LinearAlgebra
+{
+    using System;
+    using System.Globalization;
+    using MathNet.Numerics.LinearAlgebra.Double;
+
+    /// <summary>
+    /// Special numbers associated with any square matrix
+    /// </summary>
+    /// <seealso cref="http://reference.wolfram.com/mathematica/ref/Det.html">The determinant of the square matrix</seealso>
+    /// <seealso cref="http://reference.wolfram.com/mathematica/ref/Tr.html">The trace of the matrix</seealso>
+    /// <seealso cref="http://reference.wolfram.com/mathematica/ref/MatrixRank.html">The rank of the matrix</seealso>
+    public class MatrixSpecialNumbers : IExample
+    {
+        /// <summary>
+        /// Gets the name of this example
+        /// </summary>
+        public string Name
+        {
+            get
+            {
+                return "Special numbers associated with any square matrix";
+            }
+        }
+
+        /// <summary>
+        /// Gets the description of this example
+        /// </summary>
+        public string Description
+        {
+            get
+            {
+                return "Matrix properties as: Determinant, Condition Number, Rank and Trace";
+            }
+        }
+
+        /// <summary>
+        /// Run example
+        /// </summary>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Determinant">Determinant</seealso>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Rank_%28linear_algebra%29">Rank (linear algebra)</seealso>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Trace_%28linear_algebra%29">Trace (linear algebra)</seealso>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Condition_number">Condition number</seealso>
+        public void Run()
+        {
+            // Format matrix output to console
+            var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
+            formatProvider.TextInfo.ListSeparator = " ";
+
+            // Create random square matrix
+            var matrix = new DenseMatrix(5);
+            var rnd = new Random(1); 
+            for (var i = 0; i < matrix.RowCount; i++)
+            {
+                for (var j = 0; j < matrix.ColumnCount; j++)
+                {
+                    matrix[i, j] = rnd.NextDouble();
+                }
+            }
+
+            Console.WriteLine(@"Initial matrix");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 1. Determinant
+            Console.WriteLine(@"1. Determinant");
+            Console.WriteLine(matrix.Determinant());
+            Console.WriteLine();
+
+            // 2. Rank
+            Console.WriteLine(@"2. Rank");
+            Console.WriteLine(matrix.Rank());
+            Console.WriteLine();
+
+            // 3. Condition number
+            Console.WriteLine(@"2. Condition number");
+            Console.WriteLine(matrix.ConditionNumber());
+            Console.WriteLine();
+
+            // 4. Trace
+            Console.WriteLine(@"4. Trace");
+            Console.WriteLine(matrix.Trace());
+            Console.WriteLine();
+        }
+    }
+}

src/Examples/LinearAlgebra/MatrixTransposeAndInverse.cs

@@ -0,0 +1,120 @@
+// <copyright file="MatrixTransposeAndInverse.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+// Copyright (c) 2009-2010 Math.NET
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace Examples.LinearAlgebra
+{
+    using System;
+    using System.Globalization;
+    using MathNet.Numerics.LinearAlgebra.Double;
+    using MathNet.Numerics.LinearAlgebra.Generic.Factorization;
+
+    /// <summary>
+    /// Matrix transpose and inverse
+    /// </summary>
+    /// <seealso cref="http://reference.wolfram.com/mathematica/ref/Transpose.html">Transpose</seealso>
+    /// <seealso cref="http://reference.wolfram.com/mathematica/ref/Inverse.html">Inverse</seealso>
+    public class MatrixTransposeAndInverse : IExample
+    {
+        /// <summary>
+        /// Gets the name of this example
+        /// </summary>
+        public string Name
+        {
+            get
+            {
+                return "Matrix transpose and inverse";
+            }
+        }
+
+        /// <summary>
+        /// Gets the description of this example
+        /// </summary>
+        public string Description
+        {
+            get
+            {
+                return "Transpose matrix, inverse matrix, transpose-and-multiply matrix examples";
+            }
+        }
+
+        /// <summary>
+        /// Run example
+        /// </summary>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Transpose">Transpose</seealso>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Invertible_matrix">Invertible matrix</seealso>
+        public void Run()
+        {
+            // Format matrix output to console
+            var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
+            formatProvider.TextInfo.ListSeparator = " ";
+
+            // Create random square matrix
+            var matrix = new DenseMatrix(5);
+            var rnd = new Random(1);
+            for (var i = 0; i < matrix.RowCount; i++)
+            {
+                for (var j = 0; j < matrix.ColumnCount; j++)
+                {
+                    matrix[i, j] = rnd.NextDouble();
+                }
+            }
+
+            Console.WriteLine(@"Initial matrix");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 1. Get matrix inverse
+            var inverse = matrix.Inverse();
+            Console.WriteLine(@"1. Matrix inverse");
+            Console.WriteLine(inverse.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Matrix multiplied by its inverse gives identity matrix
+            var identity = matrix * inverse;
+            Console.WriteLine(@"2. Matrix multiplied by its inverse");
+            Console.WriteLine(identity.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 3. Get matrix transpose
+            var transpose = matrix.Transpose();
+            Console.WriteLine(@"3. Matrix transpose");
+            Console.WriteLine(transpose.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 4. Get orthogonal  matrix, i.e. do QR decomposition and get matrix Q
+            var orthogonal = matrix.QR().Q;
+            Console.WriteLine(@"4. Orthogonal  matrix");
+            Console.WriteLine(orthogonal.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 5. Transpose and multiply orthogonal matrix by iteslf gives identity matrix
+            identity = orthogonal.TransposeAndMultiply(orthogonal);
+            Console.WriteLine(@"Transpose and multiply orthogonal matrix by iteslf");
+            Console.WriteLine(identity.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+        }
+    }
+}

src/Examples/LinearAlgebra/MatrixTriangular.cs

@@ -0,0 +1,123 @@
+// <copyright file="MatrixTriangular.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+// Copyright (c) 2009-2010 Math.NET
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace Examples.LinearAlgebra
+{
+    using System;
+    using System.Globalization;
+    using MathNet.Numerics.LinearAlgebra.Double;
+
+    /// <summary>
+    /// Triangular matrices
+    /// </summary>
+    /// <seealso cref="http://reference.wolfram.com/mathematica/guide/PartsOfMatrices.html"/>
+    public class MatrixTriangular : IExample
+    {
+        /// <summary>
+        /// Gets the name of this example
+        /// </summary>
+        public string Name
+        {
+            get
+            {
+                return "Retrieving special forms of the matrix";
+            }
+        }
+
+        /// <summary>
+        /// Gets the description of this example
+        /// </summary>
+        public string Description
+        {
+            get
+            {
+                return "Retrieving different forms of triangular matrices from existing matrix";
+            }
+        }
+
+        /// <summary>
+        /// Run example
+        /// </summary>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Triangular_matrix">Triangular matrix</seealso>
+        public void Run()
+        {
+            // Format matrix output to console
+            var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
+            formatProvider.TextInfo.ListSeparator = " ";
+
+            // Create square matrix
+            var matrix = new DenseMatrix(10);
+            var k = 0;
+            for (var i = 0; i < matrix.RowCount; i++)
+            {
+                for (var j = 0; j < matrix.ColumnCount; j++)
+                {
+                    matrix[i, j] = k++;
+                }
+            }
+
+            Console.WriteLine(@"Initial square matrix");
+            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 1. Retrieve a new matrix containing the lower triangle of the matrix
+            var lower = matrix.LowerTriangle();
+
+            // Puts the lower triangle of the matrix into the result matrix.
+            matrix.LowerTriangle(lower);
+            Console.WriteLine(@"1. Lower triangle of the matrix");
+            Console.WriteLine(lower.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Retrieve a new matrix containing the upper triangle of the matrix
+            var upper = matrix.UpperTriangle();
+
+            // Puts the upper triangle of the matrix into the result matrix.
+            matrix.UpperTriangle(lower);
+            Console.WriteLine(@"2. Upper triangle of the matrix");
+            Console.WriteLine(upper.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 3. Retrieve a new matrix containing the strictly lower triangle of the matrix
+            var strictlylower = matrix.StrictlyLowerTriangle();
+
+            // Puts the strictly lower triangle of the matrix into the result matrix.
+            matrix.StrictlyLowerTriangle(strictlylower);
+            Console.WriteLine(@"3. Strictly lower triangle of the matrix");
+            Console.WriteLine(strictlylower.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 4. Retrieve a new matrix containing the strictly upper triangle of the matrix
+            var strictlyupper = matrix.StrictlyUpperTriangle();
+
+            // Puts the strictly upper triangle of the matrix into the result matrix.
+            matrix.StrictlyUpperTriangle(strictlyupper);
+            Console.WriteLine(@"4. Strictly upper triangle of the matrix");
+            Console.WriteLine(strictlyupper.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+        }
+    }
+}

src/Examples/LinearAlgebra/VectorArithmeticOperations.cs

@@ -0,0 +1,209 @@
+// <copyright file="VectorArithmeticOperations.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+// Copyright (c) 2009-2010 Math.NET
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace Examples.LinearAlgebra
+{
+    using System;
+    using System.Globalization;
+    using MathNet.Numerics.LinearAlgebra.Double;
+
+    /// <summary>
+    /// Basic vector arithmetic operations as "+", "-", "*", "/"
+    /// </summary>
+    /// <seealso cref="http://reference.wolfram.com/mathematica/tutorial/VectorsAndMatrices.html"/>
+    public class VectorArithmeticOperations : IExample
+    {
+        /// <summary>
+        /// Gets the name of this example
+        /// </summary>
+        public string Name
+        {
+            get
+            {
+                return "Vector Arithmetics";
+            }
+        }
+
+        /// <summary>
+        /// Gets the description of this example
+        /// </summary>
+        public string Description
+        {
+            get
+            {
+                return "Basic operations between vector/vector and vector/matrix";
+            }
+        }
+
+        /// <summary>
+        /// Run example.
+        /// </summary>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Euclidean_vector#Scalar_multiplication">Multiply vector by scalar</seealso>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Euclidean_vector#Dot_product">Multiply vector by vector (compute the dot product between two vectors)</seealso>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction">Vector addition and subtraction</seealso>
+        /// <seealso cref="http://en.wikipedia.org/wiki/Outer_product">Outer Product of two vectors</seealso>
+        public void Run()
+        {
+            // Initialize IFormatProvider to print matrix/vector data 
+            var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
+            formatProvider.TextInfo.ListSeparator = " ";
+
+            // Create vector "X"
+            var vectorX = new DenseVector(new[] { 1.0, 2.0, 3.0, 4.0, 5.0 });
+            Console.WriteLine(@"Vector X");
+            Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Create vector "Y"
+            var vectorY = new DenseVector(new[] { 5.0, 4.0, 3.0, 2.0, 1.0 });
+            Console.WriteLine(@"Vector Y");
+            Console.WriteLine(vectorY.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Multiply vector by scalar
+            // 1. Using Multiply method and getting result into different vector instance
+            var resultV = vectorX.Multiply(3.0);
+            Console.WriteLine(@"Multiply vector by scalar using method Multiply. (result = X.Multiply(3.0))");
+            Console.WriteLine(resultV.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Using operator "*"
+            resultV = 3.0 * vectorX;
+            Console.WriteLine(@"Multiply vector by scalar using operator *. (result = 3.0 * X)");
+            Console.WriteLine(resultV.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 3. Using Multiply method and updating vector itself
+            vectorX.Multiply(3.0, vectorX);
+            Console.WriteLine(@"Multiply vector by scalar using method Multiply. (X.Multiply(3.0, X))");
+            Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Multiply vector by vector (compute the dot product between two vectors)
+            // 1. Using operator "*"
+            var dotProduct = vectorX * vectorY;
+            Console.WriteLine(@"Dot product between two vectors using operator *. (result = X * Y)");
+            Console.WriteLine(dotProduct);
+            Console.WriteLine();
+
+            // 2. Using DotProduct method and getting result into different vector instance
+            dotProduct = vectorX.DotProduct(vectorY);
+            Console.WriteLine(@"Dot product between two vectors using method DotProduct. (result = X.DotProduct(Y))");
+            Console.WriteLine(dotProduct.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Pointwise multiplie vector with another vector
+            // 1. Using PointwiseMultiply method and getting result into different vector instance
+            resultV = vectorX.PointwiseMultiply(vectorY);
+            Console.WriteLine(@"Pointwise multiplie vector with another vector using method PointwiseMultiply. (result = X.PointwiseMultiply(Y))");
+            Console.WriteLine(resultV.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Using PointwiseMultiply method and updating vector itself
+            vectorX.PointwiseMultiply(vectorY, vectorX);
+            Console.WriteLine(@"Pointwise multiplie vector with another vector using method PointwiseMultiply. (X.PointwiseMultiply(Y, X))");
+            Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Pointwise divide vector with another vector
+            // 1. Using PointwiseDivide method and getting result into different vector instance
+            resultV = vectorX.PointwiseDivide(vectorY);
+            Console.WriteLine(@"Pointwise divide vector with another vector using method PointwiseDivide. (result = X.PointwiseDivide(Y))");
+            Console.WriteLine(resultV.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Using PointwiseDivide method and updating vector itself
+            vectorX.PointwiseDivide(vectorY, vectorX);
+            Console.WriteLine(@"Pointwise divide vector with another vector using method PointwiseDivide. (X.PointwiseDivide(Y, X))");
+            Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Addition
+            // 1. Using operator "+"
+            resultV = vectorX + vectorY;
+            Console.WriteLine(@"Add vectors using operator +. (result = X + Y)");
+            Console.WriteLine(resultV.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Using Add method and getting result into different vector instance
+            resultV = vectorX.Add(vectorY);
+            Console.WriteLine(@"Add vectors using method Add. (result = X.Add(Y))");
+            Console.WriteLine(resultV.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 3. Using Add method and updating vector itself
+            vectorX.Add(vectorY, vectorX);
+            Console.WriteLine(@"Add vectors using method Add. (X.Add(Y, X))");
+            Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Subtraction
+            // 1. Using operator "-"
+            resultV = vectorX - vectorY;
+            Console.WriteLine(@"Subtract vectors using operator -. (result = X - Y)");
+            Console.WriteLine(resultV.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Using Subtract method and getting result into different vector instance
+            resultV = vectorX.Subtract(vectorY);
+            Console.WriteLine(@"Subtract vectors using method Subtract. (result = X.Subtract(Y))");
+            Console.WriteLine(resultV.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 3. Using Subtract method and updating vector itself
+            vectorX.Subtract(vectorY, vectorX);
+            Console.WriteLine(@"Subtract vectors using method Subtract. (X.Subtract(Y, X))");
+            Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Divide by scalar
+            // 1. Using Divide method and getting result into different vector instance
+            resultV = vectorX.Divide(3.0);
+            Console.WriteLine(@"Divide vector by scalar using method Divide. (result = A.Divide(3.0))");
+            Console.WriteLine(resultV.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Using Divide method and updating vector itself
+            vectorX.Divide(3.0, vectorX);
+            Console.WriteLine(@"Divide vector by scalar using method Divide. (X.Divide(3.0, X))");
+            Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // Outer Product of two vectors
+            // 1. Using instanse method OuterProduct
+            var resultM = vectorX.OuterProduct(vectorY);
+            Console.WriteLine(@"Outer Product of two vectors using method OuterProduct. (X.OuterProduct(Y))");
+            Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Using static method of the Vector class
+            resultM = Vector.OuterProduct(vectorX, vectorY);
+            Console.WriteLine(@"Outer Product of two vectors using method OuterProduct. (Vector.OuterProduct(X,Y))");
+            Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+        }
+    }
+}

src/Examples/LinearAlgebra/VectorDataAccessor.cs

@@ -0,0 +1,158 @@
+// <copyright file="VectorDataAccessor.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+// Copyright (c) 2009-2010 Math.NET
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace Examples.LinearAlgebra
+{
+    using System;
+    using System.Globalization;
+    using MathNet.Numerics.LinearAlgebra.Double;
+
+    /// <summary>
+    /// Vector data access, copying and conversion examples
+    /// </summary>
+    public class VectorDataAccessor
+    {
+        /// <summary>
+        /// Gets the name of this example
+        /// </summary>
+        public string Name
+        {
+            get
+            {
+                return "Vector data access, copying and conversion";
+            }
+        }
+
+        /// <summary>
+        /// Gets the description of this example
+        /// </summary>
+        public string Description
+        {
+            get
+            {
+                return "Examples of setting/getting values of a vector, copying and conversion vector into another vector";
+            }
+        }
+
+        /// <summary>
+        /// Run example
+        /// </summary>
+        public void Run()
+        {
+            // Format vector output to console
+            var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
+            formatProvider.TextInfo.ListSeparator = " ";
+
+            // Create new empty vector
+            var vectorA = new DenseVector(10);
+            Console.WriteLine(@"Empty vector A");
+            Console.WriteLine(vectorA.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+            
+            // 1. Fill vector by data using indexer []
+            for (var i = 0; i < vectorA.Count; i++)
+            {
+                vectorA[i] = i;
+            }
+
+            Console.WriteLine(@"1. Fill vector by data using indexer []");
+            Console.WriteLine(vectorA.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 2. Fill vector by data using SetValues method
+            vectorA.SetValues(new[] { 9.0, 8.0, 7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0, 0.0 });
+            Console.WriteLine(@"2. Fill vector by data using SetValues method");
+            Console.WriteLine(vectorA.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 3. Convert Vector to double[]
+            var data = vectorA.ToArray();
+            Console.WriteLine(@"3. Convert vector to double array");
+            for (var i = 0; i < data.Length; i++)
+            {
+                Console.Write(data[i].ToString("#0.00\t", formatProvider) + @" ");
+            }
+
+            Console.WriteLine();
+            Console.WriteLine();
+
+            // 4. Convert Vector to column matrix. A matrix based on this vector in column form (one single column)
+            var columnMatrix = vectorA.ToColumnMatrix();
+            Console.WriteLine(@"4. Convert vector to column matrix");
+            Console.WriteLine(columnMatrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 5. Convert Vector to row matrix. A matrix based on this vector in row form (one single row)
+            var rowMatrix = vectorA.ToRowMatrix();
+            Console.WriteLine(@"5. Convert vector to row matrix");
+            Console.WriteLine(rowMatrix.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 6. Clone vector
+            var cloneA = vectorA.Clone();
+            Console.WriteLine(@"6. Clone vector");
+            Console.WriteLine(cloneA.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 7. Clear vector
+            cloneA.Clear();
+            Console.WriteLine(@"7. Clear vector");
+            Console.WriteLine(cloneA.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 8. Copy part of vector into another vector. If you need to copy all data then use CopoTy(vector) method.
+            vectorA.CopyTo(cloneA, 3, 3, 4);
+            Console.WriteLine(@"8. Copy part of vector into another vector");
+            Console.WriteLine(cloneA.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            // 9. Get part of vector as another vector
+            var subvector = vectorA.SubVector(0, 5);
+            Console.WriteLine(@"9. Get subvector");
+            Console.WriteLine(subvector.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+           // 10. Enumerator usage
+            Console.WriteLine(@"10. Enumerator usage");
+            foreach (var value in vectorA)
+            {
+                Console.Write(value.ToString("#0.00\t", formatProvider) + @" ");
+            }
+
+            Console.WriteLine();
+            Console.WriteLine();
+
+            // 11. Indexed enumerator usage
+            Console.WriteLine(@"11. Enumerator usage");
+            foreach (var value in vectorA.GetIndexedEnumerator())
+            {
+                Console.WriteLine(@"Index = {0}; Value = {1}", value.Key, value.Value.ToString("#0.00\t", formatProvider));
+            }
+
+            Console.WriteLine();
+        }
+    }
+}

src/Examples/LinearAlgebra/VectorInitialization.cs

@@ -0,0 +1,98 @@
+// <copyright file="VectorInitialization.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+// Copyright (c) 2009-2010 Math.NET
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace Examples.LinearAlgebra
+{
+    using System;
+    using System.Globalization;
+    using MathNet.Numerics.LinearAlgebra.Double;
+
+    /// <summary>
+    /// Vector initialization examples
+    /// </summary>
+    public class VectorInitialization : IExample
+    {
+        /// <summary>
+        /// Gets the name of this example
+        /// </summary>
+        public string Name
+        {
+            get
+            {
+                return "Vector initialization";
+            }
+        }
+
+        /// <summary>
+        /// Gets the description of this example
+        /// </summary>
+        public string Description
+        {
+            get
+            {
+                return "Examples of creating vector instances";
+            }
+        }
+
+        /// <summary>
+        /// Run example
+        /// </summary>
+        public void Run()
+        {
+            // 1. Initialize a new instance of the empty vector with a given size
+            var vector1 = new DenseVector(5);
+
+            // 2. Initialize a new instance of the vector with a given size and each element set to the given value
+            var vector2 = new DenseVector(5, 3.0);
+
+            // 3. Initialize a new instance of the vector from an array.
+            var vector3 = new DenseVector(new[] { 1.0, 2.0, 3.0, 4.0, 5.0 });
+
+            // 4. Initialize a new instance of the vector by copying the values from another.
+            var vector4 = new DenseVector(vector3);
+
+            // Format vector output to console
+            var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
+            formatProvider.TextInfo.ListSeparator = " ";
+
+            Console.WriteLine(@"Vector 1");
+            Console.WriteLine(vector1.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            Console.WriteLine(@"Vector 2");
+            Console.WriteLine(vector2.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            Console.WriteLine(@"Vector 3");
+            Console.WriteLine(vector3.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+
+            Console.WriteLine(@"Vector 4");
+            Console.WriteLine(vector4.ToString("#0.00\t", formatProvider));
+            Console.WriteLine();
+        }
+    }
+}

src/Numerics/LinearAlgebra/Generic/Matrix.cs

@@ -1002,7 +1002,7 @@ namespace MathNet.Numerics.LinearAlgebra.Generic
 
             result.SetRow(rowIndex, row);
 
-            for (var i = rowIndex + 1; i < RowCount; i++)
+            for (var i = rowIndex + 1; i < RowCount + 1; i++)
             {
                 result.SetRow(i, Row(i - 1));
             }